The filamentous cyanobacterium, Pseudanabaena, has been shown to produce reticulate patterns that are thought to be the result of its gliding motility. Similar fossilized structures found in the geological record constitute some of the earliest signs of life on Earth. It is difficult to tie these fossils, which are billions of years old, directly to the specific microorganisms that built them. Identifying the physicochemical conditions and microorganism properties that lead microbial mats to form macroscopic structures can lead to a better understanding of the conditions on Earth at the dawn of life. In this article, a cell-based model is used to simulate the formation of reticulate patterns in cultures of Pseudanabaena. A minimal system of long and flexible trichomes capable of gliding motility is shown to be sufficient to produce stable patterns consisting of a network of streams. Varying model parameters indicate that systems with little to no cohesion, high trichome density and persistent movement are conducive to reticulate pattern formation, in conformance with experimental observations.